Mathematical models and nonlinear dynamics of a linear electromagnetic motor

摘要

The aim of this paper was to construct a mathematical model of a drive system with ironless permanent magnet synchronous linear motor and to animalize the influence of the magnetic field distribution function on the model's accuracy and ease of simulation computation. The studied motor employs an U-shaped stationary guideway with permanent magnets placed perpendicularly to the motor's direction of motion and a forcer with three sets of rectangular coils subjected to alternating external electrical voltage. The system's parameters are both mechanical (number of magnets and coils, size of magnets, distances between magnets, size of coils) and electromagnetic (auxiliary magnetic field, permeability, coil's resistance). Lorentz force allows for the transition from electromagnetic parameters to mechanical force, and Faraday's law of induction creates a feedback between the forcer's speed and coils voltage. An Ampere's model of permanent magnet is used to determine the function of auxiliary magnetic field distribution throughout the stator. Two simplified distribution functions are introduced and studied. During validation, external current function is applied to each coil (serving as excitation), while the displacement of forcer in time is the output function. Model parameters are found via genetic algorithms such that the numerical solution of the model best fits experimental data. Several cases of motor operation are compared against simulation results showing good coincidence between computation and experiment.